Wind measurement by means of a multicopter

ABSTRACT

The invention relates to a multicopter, using which wind measurements can be carried out, and a method for wind measurement by means of a multicopter. The multicopter includes a number N of electric motors MOT n  for driving N propellers PROP n , a first interface for providing first parameters P 1  including: a 3D position r B  of the center of gravity B of the multicopter, the time derivatives {dot over (r)} B  and {umlaut over (r)} B , a 3D orientation o M  of the multicopter and its time derivative {dot over (o)} M ; a second interface for providing an aerodynamic power P a,n  presently generated by the respective propellers PROP n ; a first unit which, on the basis of the first parameters P 1,  on the basis of a provided model M 1  that describes dynamics of the multicopter, and an estimation determined on the basis of the model M 1  of a force screw τ e  acting externally on the multicopter, determines horizontal components (v r,x , v r,y ) of a relative speed of the multicopter in relation to air; a second unit, which, on the basis of the determined horizontal components (v r,x , v r,y ) and on the basis of the aerodynamic power P a,n , determines the vertical component (v r,z ) of the relative speed v r ; a third unit, which, on the basis of the determined horizontal components (v r,x , v r,y ), the vertical component (v r,z ), and on the basis of the parameters P 1,  determines the wind speed v w  in an inertial system; and a storage unit to store wind speeds v w (r B ) and/or a transmission unit to wirelessly transmit the wind speeds v w (r B ) to a receiver.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is the U.S. National Phase of PCT/EP2017/001190,filed on Oct. 9, 2017, which claims priority to German PatentApplication No. 10 2016 119 152.3, filed on Oct. 7, 2016, the entirecontents of which are incorporated herein by reference.

BACKGROUND Field

The invention relates to a multicopter, using which wind measurementscan be carried out, and a method, system, and storage medium for windmeasurement by means of a multicopter. In particular, the inventionrelates to a multicopter that is a free-flying drone or a free-flyingrobot driven by multiple propellers.

Related Art

Multicopters which are configured for wind measurement are known in theprior art. Thus, a multicopter is disclosed in the publication:“Simultaneous Estimation of Aerodynamic and Contact Forces in FlyingRobots: Application to Metric Wind Estimations and Collision Detection”,ICRA 2015, Seattle, Wash. USA May 2015, pages: 5290-5296 of the presentinventors: Tomic T. and Haddadin S., which, on the basis of anestimation of a force screw τ_(e) acting externally on the multicopter,enables the estimation of a wind speed. The disclosure of this article,in particular the chapters: “III Modeling” and “IV IncorporatingAerodynamics into external Wrench Estimation” is hereby explicitlyincorporated into the content of the disclosure of this description.

A controller of a multicopter is disclosed in the article “AerodynamicPower Control for Multirotor Aerial Vehicles” by Bangura M. et al., in:IEEE International Conference on Robotics and Automation (ICRA),31.05.-07.06.2014 Hong Kong, China, which has robust behavior inrelation to wind disturbance and ground effects.

A method is known from U.S. Pat. No. 8,219,267 B2, using which the windspeed can be estimated during the operation of a UAV.

SUMMARY OF THE INVENTION

The object of the present invention is to specify a multicopter and amethod for operating a multicopter, using which an improved windmeasurement is possible.

The invention results from the features of the independent claims.Advantageous refinements and embodiments are the subject matter of thedependent claims. Further features, possible applications, andadvantages of the invention result from the following description, andalso the explanation of example embodiments of the invention which areillustrated in the figures.

One aspect of the invention relates to a multicopter having: a number Nof electric motors MOT_(n) for driving N propellers PROP_(n), where n=1,2, . . . N and N≥2, a first interface for providing first parameters P1including: a 3D position r_(B)=(x_(b), y_(b), z_(b)) of the center ofgravity B of the multicopter, the time derivatives: {dot over (r)}_(B)and {umlaut over (r)}_(B), a 3D orientation o_(M)=(α_(M), β_(M), γ_(M))of the multicopter and its time derivative {dot over (o)}_(M), a secondinterface for providing an aerodynamic power P_(a,n) currently generatedby the respective propellers PROP_(n), a unit 803, which, on the basisof the first parameters P1 and/or the aerodynamic power P_(a,n) and/oran estimation of one or more force screws τ_(e) externally acting on themulticopter, determines a relative speed v_(r):=(v_(r,x), v_(r,y),v_(r,z))^(T) of the multicopter in relation to the air, a unit 805,which, on the basis of the determined relative speed v_(r):=(v_(r,x),v_(r,y), v_(r,z))^(T) and on the basis of the parameter P1, determinesthe wind speed v_(w) in an inertial system, and a storage unit forstoring the wind speeds v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)),v_(w,z)(r_(B))) determined for the locations r_(B), and/or atransmission unit for the wireless transmission of the wind speedv_(w)(r_(B)) to a receiver.

The determination of the relative speed v_(r):=(v_(r,x), v_(r,y),v_(r,z))^(T) of the multicopter in relation to the air is advantageouslyperformed by means of methods of neuronal learning and/or autonomousrobot learning.

The arrangements of the propeller planes on the multicopter arefundamentally arbitrary in this case. The determination of the relativespeed v_(r):=(v_(r,x), v_(r,y), v_(r,z))^(T) therefore includescombinations of the estimated force screw and the estimated power.

If the propeller planes are arranged essentially parallel and inparticular in one plane, the following special case thus results.

A further aspect of the invention relates to a multicopter having: anumber N of electric motors MOT_(n) for driving N propellers PROP_(n),where n=1, 2, . . . , N and N≥2, a first interface for providing firstparameters P1 including: a 3D position r_(B)=(x_(b), y_(b), z_(b)) ofthe center of gravity B of the multicopter (or providing items ofinformation from which the position r_(B)=(x_(b), y_(b), z_(b)) of thecenter of gravity B of the multicopter can be determined/estimated), thetime derivatives: {dot over (r)}_(B) and {umlaut over (r)}_(B), a 3Dorientation o_(M)=(α_(M), β_(M), γ_(M)) of the multicopter and its timederivative {dot over (o)}_(M) (the variables {dot over (r)}_(B), {umlautover (r)}_(B), o_(M)=(α_(M), β_(M), γ_(M)), {dot over (o)}_(M) areadvantageously measured (for example, by means of GPS, LIDAR, cameras,etc., one or more inertial measuring units (IMU)) etc., observed, orderived (for example, by visual odometry, sensor data fusion such asKalman filters etc.), a second interface for providing an aerodynamicpower P_(a,n) currently generated by the respective propellers PROP_(n)(which is advantageously measured or observed), a first unit, which, onthe basis of the first parameters P1, on the basis of a provided modelM1 for describing dynamics of the multicopter, and an estimationdetermined on the basis of the model M1 of a force screw τ_(e) actingexternally on the multicopter, determines horizontal components(v_(r,x), v_(r,y)) of a relative speed v_(r):=(v_(r,x), v_(r,y),v_(r,z))^(T) of the multicopter in relation to the air (for this purposefunction approximators are advantageously used, which are known from thefield of “machine learning”, for example, linear regression, neuronalnetworks, multilayer perceptrons, support vector machines (SVM) etc.), asecond unit which, on the basis of the determined horizontal components(v_(r,x), v_(r,y)), and on the basis of the aerodynamic power P_(a,n),determines the vertical component (v_(r,z)) of the relative speed v_(r),a unit, which, on the basis of the determined horizontal components(v_(r,x), v_(r,y)), the vertical component (v_(r,z)), and also on thebasis of the parameters P1, determines the wind speed v_(w), in aninertial system, a storage unit for storing the wind speedsv_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B))) determinedfor the locations r_(B) and/or a transmission unit for wirelesslytransmitting the wind speed v_(w)(r_(B)) to a receiver.

In the present case, the term “multicopter” describes an aircraft whichhas two or more drive units, in particular motor-driven propellers. Themulticopter can also have lift and/or control surfaces. The arrangementof the N propellers PROP_(n) on the multicopter is arbitrary inprinciple. Each propeller is advantageously described in its owncoordinate system. The N propellers PROP_(n) can advantageously bevectored, i.e., each propeller can be described in its own time-variablecoordinate system. The method can accordingly be generalized inprinciple to other arrangements, in which the arrangement of thepropellers is not necessarily in one plane. The corresponding requiredcombinations of the estimators is derivable in an obvious manner fromthe described common case.

In principle, the proposed method can in other words execute aregression from the external force screw τ_(e) to the relative speedv_(r), a regression from the aerodynamic powers P_(a,n) to the relativespeed v_(r), and/or a regression from the external force screw τ_(e) andthe aerodynamic powers P_(a,n) to the relative speed v_(r).

The relationship: v_(r)=r_(B)−v_(w) advantageously applies in this case,where: v_(r):=(v_(r,x), v_(r,y), v_(r,z))^(T):=relative speed of themulticopter in relation to the air, and v_(w):=(v_(w,x), v_(w,y),v_(w,z))^(T) is the wind speed.

The proposed multicopter thus solely uses the approach disclosed in thearticle indicated at the outset to determine the horizontal components(v_(r,x), v_(r,y)) of the relative speed v_(r), in which, based on amodel of the dynamics of the multicopter and an estimation generatedthereby of a force screw τ_(e) acting externally on the multicopter, anestimation of the relative speed v_(r) is performed.

The determination of the vertical component (v_(r,z)) of the relativespeed v_(r) is performed in the present case on the basis of thedetermination of the aerodynamic power of the respective motor-propellercombinations and also on the basis of the previously determinedhorizontal components (v_(r,x), v_(r,y)) of the relative speed v_(r).The proposed multicopter thus enables a more accurate and robustdetermination of wind speeds during flight. It can therefore be used, inparticular, as a flying wind sensor, which stores the determined winddata on board and/or transmits them to a ground station.

Several relationships and mathematical principles are describedhereafter, which are used for the explanation and the implementation ofthe invention.

I. Movement Equations (Rigid-Body Mechanics)

The movement equations applicable to the present multicopter canfundamentally be formulated as follows:

m{umlaut over (r)}=mge ₃ +Rf+Rf _(e),   (Eq. 1)

I{dot over (ω)}=(Iω)×ω−mg(r _(g))×R ^(T) e ₃ +m+m _(e), and   (Eq. 2)

{dot over (R)}=R(ω)×  (Eq. 3)

where:

-   m: mass of the multicopter,-   r_(B)=(x, y, z)^(T): position of the multicopter in a fixed    north-east-bottom inertial system,-   R ∈ SO(3): rotation matrix from a multicopter reference system to    the inertial system,-   I ∈    ^(3×3): moment of inertia of the multicopter,-   ^(({dot over ( )})×): skew symmetric matrix operator,-   g: acceleration of gravity,-   ω: angular speed of the multicopter,-   e₃: unity vector of the z axis in the inertial system,-   r_(g): position of the mass center of gravity of the multicopter in    the multicopter reference system,-   f: target force in the multicopter reference system,-   f_(e): external force acting on the multicopter in the multicopter    reference system,-   m: target torque in the multicopter reference system, and-   m _(e): effective torque acting externally on the multicopter in the    multicopter reference system.

In this case, there are the target force screw τ=[f^(T), m ^(T)]^(T)generated by the propeller electric motor units and the force screwτ_(e)=[f_(e) ^(T), m _(e) ^(T)]^(T) acting externally on themulticopter. In general, τ=[f^(T), m ^(T)]^(T) is dependent on the freeflow speed v_(∞) and the propeller speed ω. The term “free flow speed”v_(∞) is understood in the present case as the speed of an airflow whichis uninfluenced by the multicopter.

II. Estimation of the External Force Screw

The estimation of the force screw τ_(e)=[f_(e) ^(T), m _(e) ^(T)]^(T)acting externally on the multicopter is advantageously performed on thebasis of the following relationships:

${\hat{\tau}}_{e} = {\begin{bmatrix}{\int_{0}^{t}{{K_{I}^{f}\left( {{ma} - f - {\hat{f}}_{e}} \right)}\ {dt}}} \\{K_{I}^{m}\left( {{I\; \omega} - {\int_{0}^{t}{\left( {m + {\left( {I\; \omega} \right) \times \omega} - {{{mg}\left( r_{g} \right)} \times R^{T}e_{3}} + {\overset{\_}{\hat{m}}}_{e}} \right){dt}}}} \right.}\end{bmatrix}\mspace{14mu} \left( {{Eq}.\mspace{14mu} 4} \right)}$

where:

-   K_(I) ^(f) and K_(I) ^(m): amplification factors of filters,-   a=R^(T)({umlaut over (r)}−ge₃): acceleration measured in the    reference system of the multicopter, and-   {circumflex over (f)}_(e) and {circumflex over (m)}_(e): estimated    external force or external torque, respectively, acting on the    multicopter.

More detailed statements in this regard result, for example, from thearticle by Tomic T., “Evaluation of acceleration-based disturbanceobservation for multicopter control” in European Control Conference(ECC), 2014, pages 2937-2944.

III. Propeller Aerodynamics

The forces acting on a propeller of the multicopter are dependent on thefree flow speed v_(∞) (relative wind speed). The free flow speed v_(∞)of the n-th propeller in a reference system of the propeller can beexpressed as follows:

v _(∞) ^((n)) =R _(pb) ^((n))(R _(bi) ^((n)) v _(r) +ω×r _(n))   (Eq. 5)

wherein v_(r)={dot over (r)}_(B)−v_(w) is the true airspeed of themulticopter, v_(w) is the wind speed, R_(bi) ^((n)) is the rotationmatrix from the inertial system to the reference system of themulticopter, R_(pb) ^((n)) is the rotation matrix from the referencesystem of the multicopter to the reference system of the propeller, ω isthe angular speed of the multicopter, and r_(n) is the position of therespective propeller in relation to the reference system of themulticopter. On the basis of preservation of momentum, the followingresults for the thrust T generated by the n-th propeller

T=2ρAv_(i)U   (Eq. 6)

where: ρ:=air density, A:=area swept by the propeller, andU=∥v_(i)e₃+v_(∞)∥ is the total wake flow generated by the propeller. Theflow speed v_(i) induced by the propeller can advantageously bedetermined as follows:

v _(i) =v _(h) ²/√{square root over (v_(xy) ²+(v _(i) −v _(z))²)}.  (Eq. 7)

The solution is advantageously performed by means of a Newton-Raphsonmethod in a few steps with known v_(h) and v_(∞). For the horizontal andthe vertical component of the free flow speed, the following applies:v_(xy)=v_(∞)−v_(z) and v_(z)=e₃ ^(T)v_(∞). In hovering flight, thefollowing applies for the induced speed: v_(i)=v_(h)=√{square root over(T_(h)/2ρA)}, wherein the hovering flight thrust T_(h) results fromT_(h)=ρD⁴C_(T) ω ². The thrust coefficient C_(T) is advantageouslydetermined from static thrust measurements. D indicates the diameter ofthe respective propeller and ω indicates the propeller rotational speed.The ideal aerodynamic propeller power is given by:

P _(a)=2ρAv _(i) U(v _(i) −v _(z)).   (Eq. 8)

The aerodynamic power in forward flight in relation to the hoveringflight power is:

P _(a) /P _(h)=(v _(i) −v _(z))/v _(h)   (Eq. 9)

given by P_(h)=2ρAv_(h) ³. Deviations from the ideal behavior can betaken into consideration by introducing a factor FM between 0 and 1. Therelationship between aerodynamic power P_(a) of a drive unit (electricmotor and propeller) and the motor power P_(M) generated by an electricmotor results in this case as: P_(a)=P_(M)·FM.

IV. Model for Describing a Brushless DC Electric Motor

The following dynamic motor model is advantageously used to estimate theaerodynamic power of a drive unit.

τ_(m)=(K _(q0) −K _(q1) i _(a))i _(a)   (Eq. 10)

I _(r) {dot over (ω)} _(E)=τ_(m) −D _(r)   (Eq. 11)

where: i_(a):=motor current, ω _(E):=angular speed of the electricmotor, τ_(m):=torque of the electric motor, wherein the torque factorK_(q)(i_(a)) is advantageously modeled as follows:K_(q)(i_(a))=(K_(q0)−K_(q1)i_(a)) with the constants: K_(q0), K_(q1).I_(r) is the moment of inertia of the electric motor and D_(r) is theaerodynamic moment of friction which acts on the motor. The totalmechanical power output by the electric motor results as:P_(m)=P_(a)/FM+P_(r), where P_(m):=mechanical power of the electricmotor and P_(r):=power which is required to accelerate the electricmotor rotor, is advantageously used to determine an estimation of theaerodynamic power P_(a) as follows:

P _(m)=τ_(m) ω _(E)=(K _(q0) −K _(q1) i _(a))i _(a) ω _(E),   (Eq. 12)

P_(r)=I_(r) ω _(E) {dot over (ω)} _(E), and   (Eq. 13)

P _(a) =FM((K _(q0) −K _(q1) i _(a))i _(a) −I _(r) {dot over (ω)} _(E))ω_(E).   (Eq. 14)

In summary, this means that the motor current i_(a) is measured orestimated. The variables ω _(E) and {dot over (ω)} _(E) can also bemeasured or estimated in dependence on i_(a).

V. Estimation of the Wind Speed v_(w) Based on the Determination of anExternal Force Screw τ_(e)

As stated in the article mentioned at the outset, the wind speed can bedetermined based on the force screw τ_(e) acting externally on themulticopter. It is assumed in this case that the force screw τ_(e) maybe attributed exclusively to aerodynamic τ_(d) friction forces:τ_(e)=τ_(d), so that the fundamental aerodynamic model M1 merely has tobe inverted: τ_(d)=d(v_(r)). For simple aerodynamic models, this can beperformed via a simple relation or iteration. If one uses, for example,a linear model M1 as a basis, the following thus applies, for example:

d(v _(r))=D _(l) v _(r) Σ ω ^((n))   (Eq. 15)

where D_(l):=linear coefficient matrix. If {circumflex over(f)}_(e)=d(v_(r)) is used, the following results:

$\begin{matrix}{{v_{r}(d)} = {\frac{1}{\sum\varpi_{i}}D{\hat{f}}_{e}}} & \left( {{Eq}.\mspace{14mu} 16} \right)\end{matrix}$

where: D:=a coefficient matrix. This simple model furthermore impliesthat the multicopter has a symmetrical shape.

Alternatively, a learning-based approach can be followed. The aboverelation can also be modeled by means of a radial basis function (RBF)neuronal network. This has the advantage that the inverse relation iscoded directly in the radial basis function. The relationv_(r)=d⁻¹(τ_(e)) is advantageously modeled as a normalized RBF networkhaving K base functions:

$\begin{matrix}{v_{r} = {\frac{1}{\phi_{\sum}}W\; {\phi \left( \tau_{e} \right)}}} & \left( {{Eq}.\mspace{14mu} 17} \right)\end{matrix}$

where: W ∈

^(3×K):=matrix having weighting constants of the RBFs for each speedcomponent:

$\begin{matrix}{W = {\begin{bmatrix}w_{x}^{T} \\w_{y}^{T} \\w_{z}^{T}\end{bmatrix} = \begin{bmatrix}w_{x,1} & \ldots & w_{x,K} \\w_{y,1} & \ldots & w_{y,K} \\w_{z,1} & \ldots & w_{z,K}\end{bmatrix}}} & \left( {{Eq}.\mspace{14mu} 18} \right)\end{matrix}$

and where: φ=[φ(r₁), . . . , φ(r_(K))]^(T) of the evaluated basefunctions. The network is advantageously normalized by the factor:φ_(Σ)=Σ_(i=1) ^(K) φ(r_(i)). Gaussian base functions are advantageouslyused:

$\begin{matrix}{{\phi \left( r_{i} \right)} = {\exp \left( {{- \frac{1}{\sigma^{2}}}{{x - c_{i}}}^{2}} \right)}} & \left( {{Eq}.\mspace{14mu} 19} \right)\end{matrix}$

where σ:=form parameter, x:=the determined vector, and c_(i):=the centerof the i-th base function.

VI. Wind Measurements on the Basis of Determined Aerodynamic Powers ofthe Drive Units Each Consisting of Propeller and Electric Motor

Proceeding from the equations (Eq. 7), (Eq. 8), and (Eq. 9), theaerodynamics for a propeller can be formulated as a system of nonlinearequations F(v_(r,z), v_(r,xy), v_(i), v_(h), P_(a))=0 and F=[F₁, F₂,F₃]^(T), where:

F ₁ =v _(i) ⁴−2v _(i) ³ v _(r,z) +v _(i) ²(v _(r,xy) ² +v _(r,z) ²)−v_(h) ⁴=0,

F ₂ =v _(i) U(v _(i) −v _(r,z))−P _(a)/(2ρA _(n))=0, and

F ₃ =v _(h) ²(v _(i) −v _(r,z))−P _(a)/(2ρA _(n))=0.   (Eq. 21)

It is presumed that P_(a)/(2ρA) and v_(h) are known and the vectorx=[v_(r,x), v_(r,y), v_(r,z), v_(i)]^(T) is to be determined. Theabove-mentioned system of nonlinear equations (Eq. 21) isunder-determined, since three unknown and only two known variables arepresent (in this case, the horizontal components v_(r,x) and v_(r,y) arecoupled in v_(r,xy). A plurality of solutions of the equation system(Eq. 21) thus results. To solve this minimization problem, it isproposed that the system of the equations (Eq. 21) be expanded in such away that a plurality (number K) of “measurements” of P_(a) is integratedinto the equation system.

Overall, K measurements are thus carried out to determine theaerodynamic power P_(a,n). The aerodynamic power P_(a,n) can be producedin this case, for example, K times for a single electric motor and itspropeller. Advantageously, the K “measurements” of the aerodynamic powerP_(a,n) are performed for two or more different electric motors and thepropellers thereof. Finally, for the K different measurements, atransformation of the equation system (Eq. 21) into a common referencesystem is performed. This fundamentally enables the estimation of allthree components of the relative wind direction and the wind speed v_(i)induced by the propeller by solving the nonlinear quadratic minimizationproblem (Eq. 21).

It is presumed in this case that during the K “measurements” of theaerodynamic power P_(a), the wind speed v_(w)=[v_(w,x), v_(w,y),v_(w,z)] remains equal. If the K measurements are carried out in asufficiently short time, this assumption is thus adequately justified.Sufficiently accurate wind measurements require K determinations of theaerodynamic power, wherein it is sufficient to select K advantageously≤10, or K advantageously in the range of 3 to 8. The higher K isselected, the greater is the computing effort and accompanying this alsothe period of time in which measurements are carried out, so that as aperiod of time becomes longer, the probability of a variation of thewind in the period of time rises.

Advantageously, N measurements or determinations of the aerodynamicpower P_(a) are carried out simultaneously on the K electric motorpropeller units. If, for example, K=8 is selected and the multicopterhas four drive units, only two successive “measurements” of theaerodynamic power P_(a) are thus required per drive unit. “Measurements”of the aerodynamic power P_(a) from a variety of poses of themulticopter at different points in time in a small time window canadvantageously be combined. If the flight of the multicopter is notaggressive, i.e., the orientation of the multicopter does not changesignificantly in the measuring period of time, the free flow speed v_(∞)in the reference system of the multicopter can thus be estimatedsufficiently accurately. Overall, K “measurements” of the aerodynamicpower P_(a) are thus carried out to determine the vertical component[v_(w,z)] of the wind direction v_(w).

The state vector x to be determined for K measurements is:

x=[v _(r,x) , v _(r,y) , v _(r,z) , v _(i,1) , v _(i,2) , . . . , v_(i,K)]^(T)   (Eq. 22)

wherein the expanded equation system has to be solved:

F(v _(r,x) , v _(r,y) , v _(r,z) , v _(i,1) , v _(h,1) , P _(a,1) , . .. , v _(i,K) , v _(h,K) , P _(a,K))=0

F=[F _(1,1) , F _(2,1) , F _(3,1) , . . . , F _(1,K) , F _(2,K) , F_(3,K)]^(T)   (Eq. 23)

wherein F_(1,k), F_(2,k), F_(3,k) are evaluations of the equation system(Eq. 21) for the k-th “measurement” of the aerodynamic powers. To solvethe equation (Eq. 23), a Jacobi matrix is required. The Jacobi matrixfor the k-th measurement results as:

$\begin{matrix}{^{(k)} = \begin{bmatrix}J_{11}^{(k)} & J_{12}^{(k)} & J_{13}^{(k)} & J_{14}^{(k)} \\J_{21}^{(k)} & J_{22}^{(k)} & J_{23}^{(k)} & J_{24}^{(k)} \\J_{31}^{(k)} & J_{32}^{(k)} & J_{33}^{(k)} & J_{34}^{(k)}\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 24} \right)\end{matrix}$

where: J_(ij) ^((k))=∂ F_(i,k)/∂ x_(j,k). The expanded Jacobi matrix

∈

^(3K×K+3) can thus now be constructed. In the example case of threemeasurements (K=3), the following results: x|_(N=3)=[v_(r,x), v_(r,y),v_(r,z), v_(i,1), v_(i,2), v_(i,3)]^(T) and

$\left.  \right|_{N = 3} = {\begin{bmatrix}J_{11}^{(1)} & J_{12}^{(1)} & J_{13}^{(1)} & J_{14}^{(1)} & 0 & 0 \\J_{21}^{(1)} & J_{22}^{(1)} & J_{23}^{(1)} & J_{24}^{(1)} & 0 & 0 \\J_{31}^{(1)} & J_{32}^{(1)} & J_{33}^{(1)} & J_{34}^{(1)} & 0 & 0 \\J_{11}^{(2)} & J_{12}^{(2)} & J_{13}^{(2)} & 0 & J_{14}^{(2)} & 0 \\J_{21}^{(2)} & J_{22}^{(2)} & J_{23}^{(2)} & 0 & J_{24}^{(2)} & 0 \\J_{31}^{(2)} & J_{32}^{(2)} & J_{33}^{(2)} & 0 & J_{34}^{(2)} & 0 \\J_{11}^{(3)} & J_{12}^{(3)} & J_{13}^{(3)} & 0 & 0 & J_{14}^{(3)} \\J_{21}^{(3)} & J_{22}^{(3)} & J_{23}^{(3)} & 0 & 0 & J_{24}^{(3)} \\J_{31}^{(3)} & J_{32}^{(3)} & J_{33}^{(3)} & 0 & 0 & J_{34}^{(3)}\end{bmatrix}.}$

An expansion to K measurements is easily possible for a person skilledin the art. If measurements from various poses of the multicopter arecombined, the wind speeds resulting in each case have to be transformedinto a common reference system.

The free flow speed for the n-th propeller is advantageously defined asfollows:

$\begin{matrix}{v_{\infty}^{(n)} = {\begin{bmatrix}v_{\infty,x}^{(n)} \\v_{\infty,y}^{(n)} \\v_{\infty,z}^{(n)}\end{bmatrix} = {{R^{(n)}\begin{bmatrix}v_{\infty,x} \\v_{\infty,y} \\v_{\infty,z}\end{bmatrix}} + v_{0}^{(n)}}}} & \left( {{Eq}.\mspace{14mu} 25} \right)\end{matrix}$

wherein the transformed speeds are used to compute equations (Eq. 21)and (Eq. 24). The offset speed v₀ ^((n)) can be obtained from a poseestimation system as the difference speed between two measurements. Theoffset speed of the propeller on the basis of an angular speed of themulticopter can advantageously also be used, for example, v₀^((n))=R_(pb) ^((n)) ω×r_(n). The rotation matrix R^((n)) transforms therelative speed from the common coordinate system into the propellercoordinate system. This formulation advantageously enables theindependent determination of all three components of the free flowspeed. Furthermore, it also permits the determination of the windcomponents v_(w) for the case in which the propellers are not arrangedin a coplanar configuration on the multicopter.

If the equations “match”, a multidimensional optimization problem is tobe solved. The solution is then in the intersection of all nonlinearfunctions for which the following applies: F=0. In the general case,however, an intersection does not result for all nonlinear functions. Inthis case, a nonlinear quadratic minimization problem has to be solvedusing the following objective function:

$\begin{matrix}{\overset{\_}{f} = {\frac{1}{2}F^{T}{F.}}} & \left( {{Eq}.\mspace{14mu} 26} \right)\end{matrix}$

This is advantageously performed using a Levenberg-Marquard method. Ifan exact solution exists, f=0 applies, i.e., the intersection of F=0. Inall other cases, a quadratic minimized solution results.

The solution space of the equation (Eq. 26) contains local optima. Basedon the fundamental physics, the same measured aerodynamic powers P_(a)can occur at different wind speeds v_(w) and induced speeds v_(i). Theoptimized variables are speeds. It is therefore advisable to usephysical considerations as the foundation, to differentiate reasonablesolutions from nonsensical solutions. A multicopter has to use power togenerate thrust, which means T>0 and P_(a)>0. The induced speed v_(i) isless than the hovering flight speed v_(h). The induced speed isadvantageously restricted to a range 0<v_(i)<v_(h).

One advantageous refinement of the multicopter is distinguished in thatthe second unit is embodied and configured for the purpose of solvingthe following quadratic minimization problem or one which istransferable thereto or is equivalent in its basic concepts for a numberof a total of K measurements of the aerodynamic power P_(a,n) for f,where k=1, . . . , K and K≥1:

${(1)\mspace{14mu} \overset{\_}{f}} = {\frac{1}{2}F^{T}F}$

wherein the following applies:

F(v _(r,x) , v _(r,y) , v _(r,z) , v _(i,1) , v _(h,1) , P _(a,1) , . .. , v _(i,K) , v _(h,K) , P _(a,K))=0,   (2)

F=[F _(1,1) , F _(2,1) , F _(3,1) , . . . , F _(1,K) , F _(2,K) , F_(3,K)],   (3)

F _(1,K) =v _(i,k) ⁴−2v _(i,k) ³ v _(r,z) +v _(i,k) ²(v _(r,x) ² +v_(r,y) ² +v _(r,z) ²)−v _(h,k) ⁴=0,   (4)

F _(2,k) =v _(i,k) U _(k)(v _(i,k) −v _(r,z))−P _(a,k)/(2ρA _(n))=0,  (5)

F _(3,k) =v _(h,k) ²(v _(i,k) −v _(r,z))−P _(a,k)/(2ρA _(n))=0, and  (6)

U _(k)=√{square root over (v_(r,x) ² +v _(r,y) ²+(v _(i,k) −v_(r,z))²)}  (7)

where

-   A_(n): area swept by the n-th propeller,-   ρ: air density,-   v_(h,k)(P_(a,n,k)): induced speed of the n-th propeller in hovering    flight for the k-th measurement, and-   v_(i,k)(P_(a,n,k)): speed induced by the n-th propeller for the k-th    measurement.

Above equations (1) to (7) are described in the respective propellercoordinate system.

One advantageous refinement of the multicopter is distinguished in thatthe second unit is embodied and configured in such a way that thehorizontal components (v_(r,x), v_(r,y)) of the relative speed v_(r)determined by the first unit are taken into consideration in thenonlinear quadratic minimization problem by the following relationshipsor relationships transferable thereto:

F _(4,k) =v _(r,x,k) −v _(r,x)=0 and   (9)

F _(5,k) =v _(r,y,k) −v _(r,y)=0.   (10)

The equations (9) and (10) are described in the respective propellercoordinate system. Therefore, the speed estimated according to presentclaim 1 can be projected in the propeller coordinate system, so thatthese equations apply.

An advantageous refinement of the multicopter is distinguished in thatthe model M1 is based on the following movement equation or the model M1can be traced back to the following movement equation:

M{dot over (v)}+C(v)v+g _(M) =J ^(T)τ+τ_(e)

wherein the following applies: τ_(e)=τ_(d)(v_(r)) and v_(r)={dot over(r)}_(B)−v_(w), where

-   M: generalized mass of the multicopter,-   v: generalized speed [{dot over (r)}_(b) ^(T), ω^(T)],-   ω: angular speed of the multicopter,-   {dot over (v)}: time derivative of v,

${{{C(v)}\text{:}}\mspace{11mu} = \begin{bmatrix}0_{3{x3}} & 0_{3{x3}} \\0_{3{x3}} & {{- \left( {I\; \omega} \right)} \times}\end{bmatrix}},$

-   g_(M): weight of the multicopter,-   J: block diagonals of the Jakobi matrix,-   τ: target force screw [f^(T), m ^(T)] to be generated by the    electric motors MOT_(n),-   τ_(e): force screw [f_(e) ^(T), m _(e) ^(T)] acting externally on    the multicopter,-   τ_(d)(v_(r)): external force screw generated exclusively by air    friction,-   v_(r):=(v_(r,x), v_(r,y), v_(r,z))^(T) relative speed of the    multicopter in relation to the air, and-   v_(w):=(v_(w,x), v_(w,y), v_(w,z))^(T) wind speed.

One advantageous refinement of the multicopter is distinguished in thata control system is provided for controlling and regulating the electricmotors MOT_(n), wherein the control system is embodied and configured insuch a way that the electric motors MOT_(n) are regulated in such a waythat the projection of the determined wind speed v_(w) on the directionof axis of rotation of the propellers PROP_(n) is maximized.

The fundamental optimization problem can also be mathematicallyformulated. For this purpose, an orientation o* has to be determinedwhich minimizes the condition number of the Jakobi matrix, by o*=argminK(J), wherein K is the condition number.

Trajectory planning can advantageously be used for this purpose inparticular and/or the control of the multicopter can be adapted to theoptimal wind estimation. The solution can also be generated by gradientmethods, potential-based methods, or other equivalent mathematicalsolutions.

The accuracy of the wind measurement is enhanced and the robustness ofthe measurement is improved by this measure.

A 3D acceleration sensor and a gyroscope and also a positiondetermination system are advantageously provided in the multicopter andare connected to the first interface for determining the firstparameters P1. The position determination system is advantageously asatellite navigation system and/or an optical navigation system.

One advantageous refinement of the multicopter is distinguished in thatfor the determination of the aerodynamic power P_(a,n) per electricmotor MOT_(n), a motor current sensor, a motor rotational speed sensor,or a motor rotational speed estimator are provided, and also a unitwhich determines the aerodynamic power P_(a,n) on the basis of apredetermined model M2 for describing the propeller dynamic range, thedetected motor currents, and motor rotational speeds. At least onecorresponding model M2 was already explained above.

A further aspect of the invention relates to methods for measuring awind speed v_(w) using a multicopter, wherein the multicopter has anumber N of electric motors MOT_(n) for driving N propellers PROP_(n),where n=1, 2, . . . , N and N≥2, including the following steps:providing first parameters P1 including: a 3D position r_(B)=(x_(b),y_(b), z_(b)) of the center of gravity B of the multicopter, the timederivatives: {dot over (r)}_(B) and {umlaut over (r)}_(B), a 3Dorientation o_(M)=(α_(M), β_(M), γ_(M)) of the multicopter and its timederivative {dot over (o)}_(M), providing an aerodynamic power P_(a,n)currently generated by the respective propellers PROP_(n) on the basisof the first parameters P1 and/or the aerodynamic power P_(a,n) and/oran estimation of one or more force screws τ_(e) acting externally on themulticopter, determining a relative speed v_(r):=(v_(r,x), v_(r,y),v_(r,z))^(T) of the multicopter in relation to the air on the basis ofthe determined relative speed v_(r):=(v_(r,x), v_(r,y), v_(r,z))^(T) andon the basis of the parameters P1, determining the wind speed v_(w) inan inertial system, and storing the wind speedsv_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B))) determinedfor the locations r_(B), and/or transmitting the wind speed v_(w)(r_(B))to a receiver.

A further aspect of the present invention relates to a method formeasuring a wind speed v_(w) using a multicopter, wherein themulticopter has a number N of electric motors MOT_(n) for driving Npropellers PROP_(n), where n=1, 2, . . . , N and N≥2 including thefollowing steps.

In one step, a provision of first time-dependent parameters P1 isperformed, including a 3D position r_(B)=(x_(b), y_(b), z_(b)) of thecenter of gravity B of the multicopter (or providing pieces ofinformation from which the position r_(B)=(x_(b), y_(b), z_(b)) of thecenter of gravity B of the multicopter can be determined/estimated), thetime derivatives: {dot over (r)}_(B) and {umlaut over (r)}_(B), a 3Dorientation o_(M)=(α_(M), β_(M), γ_(M)) of the multicopter and the timederivative {dot over (o)}_(M) (the variables {dot over (r)}_(B), {umlautover (r)}_(B), o_(M)=(α_(M), β_(M), γ_(M)), {dot over (o)}_(M) areadvantageously measured (for example, by means of GPS, LIDAR, cameras,etc., one or more inertial measuring units (IMU)) etc., observed orderived (for example, by visual odometry, sensor data fusion such asKalman filters etc.). In a further step, a provision of an aerodynamicpower P_(a,n) generated by the respective propellers PROP_(n) isperformed (which is advantageously measured or observed). In a furtherstep, on the basis of the first parameters P1 and/or a provided model M1for describing dynamics of the multicopter and/or an estimationdetermined on the basis of the model M1 of one or more force screwsτ_(e) acting externally on the multicopter, a determination is performedof horizontal components (v_(r,x), v_(r,y)) of a relative speed v_(r) ofthe multicopter in relation to the air (for this purpose functionalapproximators are advantageously used, which are known from the field of“machine learning”, for example, linear regression, neuronal networks,multilayer perceptrons, deep neuronal networks, convolution networks,recurrent networks, for example, LSTM networks, support vector machines(SVM) etc.). In a further step, on the basis of the determinedhorizontal components (v_(r,x), v_(r,y)) and the aerodynamic powerP_(a,n), a determination is performed of the vertical component(v_(r,z)) of the relative speed v_(r). In a further step, on the basisof the determined relative speed v_(r)=(v_(r,x), v_(r,y), v_(r,z)) andon the basis of the parameters P1, a determination is performed of thewind speed v_(w) in an inertial system. Finally, storage is performed ofthe wind speed determined for r_(B): v_(w)(r_(B))=(v_(w,x)(r_(B)),v_(w,y)(r_(B)), v_(w,z)(r_(B))) and/or transmission of the wind speed:v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B))) to areceiver.

The horizontal components (v_(r,x) v_(r,y)) are thus determined bymeasuring the force screw acting externally on the multicopter using theequations (Eq. 16) and (Eq. 17). Based on the determined horizontalcomponents (v_(r,x) v_(r,y)) and a determined aerodynamic power P_(a),the vertical component (v_(r,z)) is determined.

Finally, the three-dimensional wind speed can be determined, stored,transmitted, and possibly subsequently output by way of the relationshipv_(r)={dot over (r)}−v_(w).

One advantageous refinement of the proposed method is distinguished inthat the following nonlinear quadratic minimization problem or onetransferable thereto is solved for a number of a total of K measurementsof the aerodynamic power P_(a,n) for f, where k=1, 2, . . . , K and K≥1:

${(1)\mspace{14mu} \overset{\_}{f}} = {\frac{1}{2}F^{T}F}$

wherein the following applies:

F(v _(r,x) , v _(r,y) , v _(r,z) , v _(i,1) , v _(h,1) , P _(a,1) , . .. , v _(i,K) , v _(h,K) , P _(a,K))=0,   (2)

F=[F _(1,1) , F _(2,1) , F _(3,1) , . . . , F _(1,K) , F _(2,K) , F_(3,K)],   (3)

F _(1,K) =v _(i,k) ⁴−2v _(i,k) ³ v _(r,z) +v _(i,k) ²(v _(r,x) ² +v_(r,y) ² +v _(r,z) ²)−v _(h,k) ⁴=0,   (4)

F _(2,k) =v _(i,k) U _(k)(v _(i,k) −v _(r,z))−P _(a,k)/(2ρA _(n))=0,  (5)

F _(3,k) =v _(h,k) ²(v _(i,k) −v _(r,z))−P _(a,k)/(2ρA _(n))=0, and  (6)

U _(k)=√{square root over (v_(r,x) ² +v _(r,y) ²+(v _(i,k) −v_(r,z))²)}  (7)

where

-   A_(n): area swept by the n-th propeller,-   ρ: air density,-   v_(h,k)(P_(a,n,k)): induced speed of the n-th propeller in hovering    flight for the k-th measurement, and-   v_(i,k)(P_(a,n,k)): speed induced by the n-th propeller for the k-th    measurement.

Above equations (1) to (7) are described in the respective propellercoordinate system.

One advantageous refinement of the proposed method is distinguished inthat the determined horizontal components (v_(r,x), v_(r,y)) are takeninto consideration in the nonlinear quadratic minimization problem bythe following relationships or relationships transferable thereto:

F _(4,k) =v _(r,x,k) −v _(r,x)=0 and   (9)

F _(5,k) =v _(r,y,k) −v _(r,y)=0.   (10)

Equations (9) and (10) are described in the respective propellercoordinate system. Therefore, the speed estimated according to presentclaim 1 can be projected into the propeller coordinate system so thatthese equations apply.

One advantageous refinement of the proposed method is distinguished inthat the model M1 is based on the following movement equation or themodel M1 can be traced back to the following movement equation:

M{dot over (v)}+C(v)v+g _(M) =J ^(T)τ+τ_(e)

wherein the following applies: τ_(e)=τ_(d)(v_(r)) and v_(r)={dot over(r)}_(B)−v_(w), where

-   M: generalized mass of the multicopter,-   v: generalized speed [{dot over (r)}_(b) ^(T), ω^(T)],-   ω: angular speed of the multicopter,-   {dot over (v)}: time derivative of v,

${{{C(v)}\text{:}}\mspace{11mu} = \begin{bmatrix}0_{3{x3}} & 0_{3{x3}} \\0_{3{x3}} & {{- \left( {I\; \omega} \right)} \times}\end{bmatrix}},$

-   g_(M): weight of the multicopter,-   J: block diagonals of Jakobi matrix,-   τ: target force screw [f^(T), m ^(T)] to be generated by the    electric motors MOT_(n),-   τ_(e): force screw [f_(e) ^(T), m _(e) ^(T)] acting externally on    the multicopter,-   τ_(d)(v_(r)): external force screw generated exclusively by air    friction,-   v_(r): =(v_(r,x), v_(r,y), v_(r,z))^(T) relative speed of the    multicopter in relation to the air, and-   v_(w): =(v_(w,x), v_(w,y), v_(w,z))^(T) wind speed.

One advantageous refinement of the proposed method is distinguished inthat a control system is provided for controlling and regulating theelectric motors MOT_(n), wherein the electric motors MOT_(n) areregulated in such a way that the projection of the wind speed v_(w) onthe direction of the axis of rotation of the propellers is maximized.

One advantageous refinement of the proposed method is distinguished inthat for the determination of the aerodynamic power P_(a,n) per electricmotor MOT_(n), a motor current and a motor rotational speed aredetermined, and, on the basis of a predetermined model M2 for describingthe propeller dynamic range, the detected motor currents, and motorrotational speeds, the aerodynamic power P_(a,n) is determined.

One advantageous refinement of the proposed method is distinguished inthat the determination of the horizontal components (v_(r,x), v_(r,y))is performed by means of a model of the aerodynamic force screw, whichdescribes the dependence v_(r)(τ_(e)).

One advantageous refinement of the proposed method is distinguished inthat the nonlinear quadratic minimization problem is solved by means ofa nonlinear optimization method (for example, Levenberg-Marquardt).

A further aspect of the invention relates to a computer system having adata processing device, wherein the data processing device is designedin such a way that a method as described above is executed on the dataprocessing device.

A further aspect of the invention relates to a digital storage mediumhaving electronically readable control signals, wherein the controlsignals can interact with a programmable computer system so that amethod as described above is executed.

A further aspect of the invention relates to a computer program producthaving program code stored on a machine-readable carrier for carryingout the method as described above with the program code executed on adata processing device.

A further aspect of the invention relates to a computer program havingprogram code for carrying out the method as described above when theprogram runs on a data processing device. For this purpose, the dataprocessing device can be designed as an arbitrary computer system knownfrom the prior art.

A further aspect of the invention relates to a system including two ormore multicopters as described above, wherein the multicopters are eachalso embodied and configured for bilateral data exchange with oneanother in a data network and the multicopters transmit the respectivedetermined wind speed: v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)),v_(w,z)(r_(B))) to the respective other multicopter. The data exchangepreferably takes place via radio and/or optical data transmission.

The multicopters are advantageously embodied as agents or softbots forwireless communication in the data network. The term “agent” is used inthe present case in the following meaning: “computer system which islocated in a specific environment and is capable of carrying outindependent actions in this environment to achieve its (predetermined)goals”.

One advantageous refinement of the proposed method is distinguished inthat the control system for controlling and regulating the electricmotors MOT_(n) of the respective multicopter is embodied and configuredin such a way that determined wind speeds transmitted from the othermulticopters: v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)),v_(w,z)(r_(B))) are taken into consideration in the regulation andmovement planning.

One advantageous refinement of the proposed method is distinguished inthat the multicopters transmit the positions r_(B) of the center ofgravity B and/or the time derivatives: {dot over (r)}_(B) and/or {umlautover (r)}_(B) and/or the 3D orientation o_(M) and/or its time derivative{dot over (o)}_(M) of the respective multicopter and/or the force screwsτ_(e) acting externally on the respective multicopter and/or theaerodynamic power P_(a,n) to the respective other multicopters.

One advantageous refinement of the proposed system is distinguished inthat one or more multicopters and/or a control center, which isconfigured for the data exchange with the multicopters in the datanetwork, is/are configured and embodied to solve an optimization problemaccording to claim 2. This enables in particular the proposed system tobe used as a distributed wind estimator, in which a correspondingequation system is prepared, which takes into consideration all or someof the multicopters (agents), and an optimization problem is solved, forexample, as in present claim 2. The learning of the regression via theexample above-mentioned methods can also be applied to the multicopterscenario.

Further advantages, features, and details result from the followingdescription in which—possibly with reference to the drawings—at leastone example embodiment is described in detail. Identical, similar,and/or functionally-identical parts are provided with identicalreference signs.

BRIEF DESCRIPTION OF THE DRAWINGS

In the figures:

FIG. 1 shows a diagram to illustrate the variables used to describe thedynamics of the multicopter,

FIG. 2 shows a schematic illustration of the construction of amulticopter according to the invention, and

FIG. 3 shows a schematic illustration of a flow chart of a methodaccording to the invention.

DETAILED DESCRIPTION

FIG. 1 shows a diagram to illustrate the variables and reference systemsused to describe the dynamics of the multicopter. The reference system Bof the multicopter is located at the position r having an orientation Rin the inertial system I and is subjected to the wind speed v_(w). Thiswind generates, due to aerodynamic forces in dependence on the relativespeed v_(r) of the multicopter in relation to the air, an external forcescrew τ_(e)=[f_(e) ^(T), m _(e) ^(T)]^(T). The propellers rotate at anangular speed ω=[ω ₁, ω ₂, ω ₃, ω ₄]^(T) and generate a target forcescrew τ=[f^(T), m ^(T)]^(T) due to the thrusts T_(i) and frictiontorques Q_(i). The other cumulative specifications are self-explanatoryin conjunction with the above description.

FIG. 2 shows a schematic illustration of the construction of amulticopter according to the invention. In the present case, themulticopter includes a number N=4 electric motors MOT_(n) for drivingN=4 propellers PROP_(n), a first interface 101 for providing firstparameters P1 including: a 3D position r_(B)=(x_(b), y_(b), z_(b)) ofthe center of gravity B of the multicopter, the time derivatives: {dotover (r)}_(B) and {umlaut over (r)}_(B), a 3D orientation o_(M)=(α_(M),β_(M), γ_(M)) of the multicopter and its time derivative {dot over(o)}_(M), a second interface 102 for providing an aerodynamic powerP_(a,n) currently generated by the respective propellers PROP_(n), and afirst unit 103, which, on the basis of the first parameters P1, on thebasis of a provided model M1 for describing dynamics of the multicopter,and an estimation determined on the basis of the model M1 of a forcescrew τ_(e) acting externally on the multicopter, determines horizontalcomponents (v_(r,x), v_(r,y)) of a relative speed v_(r):=(v_(r,x),v_(r,y), v_(r,z))^(T) of the multicopter in relation to the air.

The multicopter furthermore includes a second unit 104, which, on thebasis of the determined horizontal components (v_(r,x), v_(r,y)) and onthe basis of the aerodynamic power P_(a,n), determines the verticalcomponent (v_(r,z)) of the relative speed v_(r), a third unit 105,which, on the basis of the determined horizontal components (v_(r,x),v_(r,y)), the vertical component (v_(r,z)), and on the basis of theparameters P1, determines the wind speed v_(w) in an inertial system, astorage unit 106 for storing the wind speedsv_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B))) determinedfor the locations r_(B) and a transmission unit 107 for the wirelesstransmission of the wind speed v_(w)(r_(B)) to a receiver (not shown).

FIG. 3 shows a schematic illustration of a flow chart of a methodaccording to the invention for measuring a wind speed v_(w) using amulticopter, wherein the multicopter has a number N of electric motorsMOT_(n) for driving N propellers PROP_(n), where n=1, 2, . . . , N andN≥2. The method includes the following steps. In a step 201 a provisionis performed of first time-dependent parameters P1 including a 3Dposition r_(B)=(x_(b), y_(b), z_(b)) of the center of gravity B of themulticopter, the time derivatives: {dot over (r)}_(B) and {umlaut over(r)}_(B), a 3D orientation o_(M)=(α_(M), β_(M), γ_(M)) of themulticopter, and the time derivative {dot over (o)}_(M). In a furtherstep 202, a provision is performed of an aerodynamic power P_(a,n)generated by the respective propellers PROP_(n). In a further step 203,on the basis of the first parameters P1, a provided model M1 fordescribing dynamics of the multicopter, and an estimation determined onthe basis of the model M1 of a force screw τ_(e) acting externally onthe multicopter, a determination is performed of horizontal components(v_(r,x), v_(r,y)) of a relative speed v_(r) of the multicopter inrelation to the air. In a further step 204, on the basis of thedetermined horizontal components (v_(r,x), v_(r,y)) and the aerodynamicpower P_(a,n), a determination of the vertical component (v_(r,z)) ofthe relative speed v_(r), on the basis of the determined relative speedv_(r)=(v_(r,x), v_(r,y), v_(r,z)) and on the basis of the parameters P1,a determination is performed of the wind speed v_(w) in an inertialsystem. In a further step 205, a storage is performed of the wind speed:v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B))) determinedfor r_(B). In a further step 206, a transmission is performed of thewind speed: v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)),v_(w,z)(r_(B))) to a receiver.

Although the invention was illustrated and explained in greater detailby the preferred example embodiments, the invention is not thusrestricted by the disclosed examples and other variations can be derivedtherefrom by a person skilled in the art without leaving the scope ofprotection of the invention. It is therefore clear that a variety ofpossible variations exists. It is also clear that embodiments mentionedby way of example actually only represent examples which are not to beinterpreted in any way as a limitation of, for example, the scope ofprotection, the possible applications, or the configurations of theinvention. Rather, the above description and the description of thefigures make a person skilled in the art capable of implementing theexample embodiments in concrete form, wherein a person skilled in theart, aware of the disclosed concept of the invention, can performmanifold modifications, for example, with respect to the function or thearrangement of individual elements mentioned in an example embodiment,without leaving the scope of protection, which is defined by the claimsand the legal equivalents thereof, for example, more extensiveexplanations in the description.

LIST OF REFERENCE NUMERALS

101 first interface

102 second interface

103 first unit

104 second unit

105 third unit

106 storage unit

107 transmission unit

201-206 method steps

1. A multicopter having: a number N of electric motors MOT_(n) to driveN propellers PROP_(n), where n=1, 2, . . . N and N≥2; a first interfaceto provide first parameters P1 comprising: a 3D position r_(B)=(x_(b),y_(b), z_(b)) of a center of gravity B of the multicopter, timederivatives {dot over (r)}_(B) and {umlaut over (r)}_(B), a 3Dorientation o_(M)=(α_(M), β_(M), γ_(M)) of the multicopter, and a timederivative {dot over (o)}_(M) of the 3D orientation o_(M); a secondinterface to provide an aerodynamic power P_(a,n) currently generated byrespective propellers PROP_(n); a multicopter speed determination unit,which, on the basis of the first parameters P1 and/or the aerodynamicpower P_(a,n) and/or an estimation of one or more force screws τ_(e)externally acting on the multicopter, determines a relative speedv_(r):=(v_(r,x), v_(r,y), v_(r,z))^(T) of the multicopter in relation toair; a wind speed determination unit, which, on the basis of thedetermined relative speed v_(r):=(v_(r,x), v_(r,y), v_(r,z))^(T) and onthe basis of the parameters P1, determines a wind speed v_(w) in aninertial system; and a storage unit to store wind speedsv_(w)(r_(B))=v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B))) determinedfor positions r_(B), and/or a transmission unit to wirelessly transmitthe wind speeds v_(w)(r_(B)) to a receiver.
 2. (canceled)
 3. Themulticopter as claimed in claim 1, wherein the multicopter speeddetermination unit is embodied and configured to solve the followingnonlinear quadratic minimization problem for a number of a total of Kmeasurements of the aerodynamic power P_(a,n) for f where k=1, . . . , Kand k≥1: ${(1)\mspace{14mu} \overset{\_}{f}} = {\frac{1}{2}F^{T}F}$wherein the following applies:F(v _(r,x) , v _(r,y) , v _(r,z) , v _(i,1) , v _(h,1) , P _(a,1) , . .. , v _(i,K) , v _(h,K) , P _(a,K))=0,   (2)F=[F _(1,1) , F _(2,1) , F _(3,1) , . . . , F _(1,K) , F _(2,K) , F_(3,K)],   (3)F _(1,K) =v _(i,k) ⁴−2v _(i,k) ³ v _(r,z) +v _(i,k) ²(v _(r,x) ² +v_(r,y) ² +v _(r,z) ²)−v _(h,k) ⁴=0,   (4)F _(2,k) =v _(i,k) U _(k)(v _(i,k) −v _(r,z))−P _(a,k)/(2ρA _(n))=0,  (5)F _(3,k) =v _(h,k) ²(v _(i,k) −v _(r,z))−P _(a,k)/(2ρA _(n))=0, and  (6)U _(k)=√{square root over (v_(r,x) ² +v _(r,y) ²+(v _(i,k) −v_(r,z))²)}  (7) where A_(n): area swept by the n-th propeller, ρ: airdensity, v_(h,k)(P_(a,n,k)): induced speed of the n-th propeller inhovering flight for the k-th measurement, and v_(i,k)(P_(a,n,k)): speedinduced by the n-th propeller for the k-th measurement.
 4. Themulticopter as claimed in claim 1, wherein the multicopter speeddetermination unit is embodied and configured in such a way that adetermined horizontal component (v_(r,x), v_(r,y)) of the relative speedv_(r) is taken into consideration in the nonlinear quadraticminimization problem by the following relationships:F _(4,k) =v _(r,x,k) −v _(r,x)=0, and   (9)F _(5,k) =v _(r,y,k) −v _(r,y)=0.   (10)
 5. (canceled)
 6. Themulticopter as claimed in claim 1, wherein the multicopter furthercomprises a control system to control and regulate the electric motorsMOT_(n), wherein the control system is embodied and configured in such away that the electric motors MOT_(n) are regulated in such a way thatprojection of the wind speed v_(w) on direction of an axis of rotationof the propellers PROP_(n) is maximized.
 7. The multicopter as claimedin claim 1, in which, to determine the aerodynamic power P_(a,n) perelectric motor MOT_(n), the multicopter further comprises: a motorcurrent sensor, a motor rotational speed sensor, or a motor rotationalspeed estimator; and an aerodynamic power determination unit which, onthe basis of a predetermined model M2 that describes propeller dynamicrange, detected motor currents, and motor rotational speeds, determinesthe aerodynamic power P_(a,n).
 8. A method of measuring wind speed v_(w)using a multicopter, wherein the multicopter has a number N of electricmotors MOT_(n) for driving N propellers PROP_(n), where n=1, 2, . . . ,N and N≥2, the method comprising: providing first parameters P1comprising: a 3D position r_(B)=(x_(b), y_(b), z_(b)) of a center ofgravity B of the multicopter, time derivatives {dot over (r)}_(B) and{umlaut over (r)}_(B), a 3D orientation o_(M)=(α_(M), β_(M), γ_(M)) ofthe multicopter, and a time derivative {dot over (o)}_(M) of the 3Dorientation o_(M); providing an aerodynamic power P_(a,n) presentlygenerated by the respective propellers PROP_(n); on the basis of thefirst parameters P1 and/or the aerodynamic power P_(a,n) and/or anestimation of one or more force screws τ_(e) acting externally on themulticopter, determining a relative speed v_(r):=(v_(r,x), v_(r,y),v_(r,z)) of the multicopter in relation to air; on the basis of thedetermined relative speed v_(r):=(v_(r,x), v_(r,y), v_(r,z))^(T) and onthe basis of the parameters P1, determining wind speed v_(w) in aninertial system; and storing wind speeds v_(w)(r_(B))=(v_(w,x)(r_(B)),v_(w,y)(r_(B)), v_(w,z)(r_(B))) determined for positions r_(B) and/orwirelessly transmitting the wind speeds v_(w)(r_(B)) to a receiver. 9.(canceled)
 10. The method as claimed in claim 8, wherein the methodfurther comprises: providing a control system to control and regulatethe electric motors MOT_(n); and regulating the electric motors MOT_(n)in such a way that projection of the wind speed v_(w) on direction of anaxis of rotation of the propellers is maximized.
 11. The method asclaimed in claim 8, in which to determine the aerodynamic power P_(a,n)per electric motor MOT_(n), the method further comprises: determining amotor current and a motor rotational speed; and on the basis of apredetermined model M2 that describes the propeller dynamic range,detected motor currents, and motor rotational speeds, determining theaerodynamic power P_(a,n). 12.-15. (canceled)
 16. A system comprisingtwo or more multicopters as claimed in claim 1, wherein the multicoptersare each embodied and configured to exchange data with one another in adata network and the multicopters transmit respectively determined windspeed: v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B))) torespective other multicopters.
 17. The system as claimed in claim 16,wherein the multicopters are embodied as agents or softbots for wirelesscommunication in the data network.
 18. The system as claimed in claim16, wherein the system comprises a control system to control andregulate the electric motors MOT_(n) of a respective multicopter,wherein the control system is embodied and configured in such a way thatdetermined wind speeds transmitted from other multicopters:v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B))) are takeninto consideration in regulation of the electric motors MOT_(n) of therespective multicopter.
 19. The system as claimed in claim 16, whereinthe multicopters transmit positions r_(B) of the center of gravity Band/or the time derivatives: {dot over (r)}_(B) and/or {umlaut over(r)}_(B) and/or the 3D orientation o_(M) and/or the time derivative {dotover (o)}_(M) of a respective multicopter and/or the force screws τ_(e)acting externally on a respective multicopter and/or the aerodynamicpower P_(a,n) to respective other multicopters.
 20. The system asclaimed in claim 16, wherein one or more multicopters and/or a controlcenter, which is configured for data exchange with the multicopters inthe data network, is/are configured and embodied to solve anoptimization problem according to claim
 1. 21. A multicopter having: anumber N of electric motors MOT_(n) to drive N propellers PROP_(n),where n=1, 2, . . . , N and N≥2; a first interface to provide firstparameters P1 comprising: a 3D position r_(B)=(x_(b), y_(b), z_(b)) of acenter of gravity B of the multicopter, time derivatives {dot over(r)}_(B) and {umlaut over (r)}_(B), a 3D orientation o_(M)=(α_(M),β_(M), γ_(M)) of the multicopter, and a time derivative {dot over(o)}_(M) of the 3D orientation o_(M); a second interface to provide anaerodynamic power P_(a,n) currently generated by respective propellersPROP_(n); a first unit, which, on the basis of the first parameters P1and/or on the basis of a provided model M1 that describes dynamics ofthe multicopter, and/or an estimation determined on the basis of themodel M1 of a force screw τ_(e) acting externally on the multicopter,determines horizontal components (v_(r,x), v_(r,y)) of a relative speedv_(r):=(v_(r,x), v_(r,y), v_(r,z))^(T) of the multicopter in relation toair; a second unit which, on the basis of the determined horizontalcomponents (v_(r,x), v_(r,y)) and on the basis of the aerodynamic powerP_(a,n), determines the vertical component (v_(r,z)) of the relativespeed v_(r); a third unit, which, on the basis of the determinedhorizontal components (v_(r,x), v_(r,y)), the vertical component(v_(r,z)), and also on the basis of the parameters P1 determines a windspeed v_(w) in an inertial system; and a storage unit to store windspeeds v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B)))determined for positions r_(B) and/or a transmission unit to wirelesslytransmit transmission of wind speed v_(w)(r_(B)) to a receiver.
 22. Themulticopter as claimed in claim 21, wherein the second unit is embodiedand configured to solve the following nonlinear quadratic minimizationproblem for a number of a total of K measurements of the aerodynamicpower P_(a,n) for f where k=1, . . . , K and k≥1:${(1)\mspace{14mu} \overset{\_}{f}} = {\frac{1}{2}F^{T}F}$ whereinthe following applies:F(v _(r,x) , v _(r,y) , v _(r,z) , v _(i,1) , v _(h,1) , P _(a,1) , . .. , v _(i,K) , v _(h,K) , P _(a,K))=0,   (2)F=[F _(1,1) , F _(2,1) , F _(3,1) , . . . , F _(1,K) , F _(2,K) , F_(3,K)],   (3)F _(1,K) =v _(i,k) ⁴−2v _(i,k) ³ v _(r,z) +v _(i,k) ²(v _(r,x) ² +v_(r,y) ² +v _(r,z) ²)−v _(h,k) ⁴=0,   (4)F _(2,k) =v _(i,k) U _(k)(v _(i,k) −v _(r,z))−P _(a,k)/(2ρA _(n))=0,  (5)F _(3,k) =v _(h,k) ²(v _(i,k) −v _(r,z))−P _(a,k)/(2ρA _(n))=0, and  (6)U _(k)=√{square root over (v_(r,x) ² +v _(r,y) ²+(v _(i,k) −v_(r,z))²)}  (7) where A_(n): area swept by the n-th propeller, ρ: airdensity, v_(h,k)(P_(a,n,k)): induced speed of the n-th propeller inhovering flight for the k-th measurement, and v_(i,k)(P_(a,n,k)): speedinduced by the n-th propeller for the k-th measurement.
 23. Themulticopter as claimed in claim 21, wherein the second unit is embodiedand configured in such a way that a determined horizontal component(v_(r,x), v_(r,y)) of the relative speed v_(r) is taken intoconsideration in the nonlinear quadratic minimization problem by thefollowing relationships:F _(4,k) =v _(r,x,k) −v _(r,x)=0, and   (9)F _(5,k) =v _(r,y,k) −v _(r,y)=0.   (10)
 24. The multicopter as claimedin claim 22, in which in the first unit, the model M1 is based on thefollowing movement equation or the model M1 can be traced back to thefollowing movement equation:M{dot over (v)}+C(v)v+g _(M) =J ^(T)τ+τ_(e)   (1) wherein the followingapplies: τ_(e)=τ_(d)(v_(r)) and v_(r)={dot over (r)}_(B)−v_(w) M:generalized mass of the multicopter, v: generalized speed [{dot over(r)}_(b) ^(T), ω^(T)], ω: angular speed of the multicopter, {dot over(v)}: time derivative of v,${{{C(v)}\text{:}}\mspace{11mu} = \begin{bmatrix}0_{3{x3}} & 0_{3{x3}} \\0_{3{x3}} & {{- \left( {I\; \omega} \right)} \times}\end{bmatrix}},$ gM: weight of the multicopter, J: block diagonals ofthe Jakobi matrix, τ: target force screw [f^(T), m^(T)] to be generatedby the electric motors MOT_(n), τ_(e): force screw [f_(e) ^(T), m_(e)^(T)] acting externally on the multicopter, τ_(d)(v_(r)): external forcescrew generated exclusively by air friction, v_(r): =(v_(r,x), v_(r,y),v_(r,z))^(T) relative speed of the multicopter in relation to the air,and v_(w): =(v_(w,x), v_(w,y), v_(w,z))^(T) wind speed.
 25. Themulticopter as claimed in claim 21, wherein the multicopter furthercomprises a control system to control and regulate the electric motorsMOT_(n), wherein the control system is embodied and configured in such away that the electric motors MOT_(n) are regulated in such a way thatprojection of the wind speed v_(w) on direction of an axis of rotationof the propellers PROP_(n) is maximized.
 26. The multicopter as claimedin claim 21, in which, to determine the aerodynamic power P_(a,n) perelectric motor MOT_(n), the multicopter further comprises: a motorcurrent sensor, a motor rotational speed sensor, or a motor rotationalspeed estimator; and an aerodynamic power determination unit which, onthe basis of a predetermined model M2 that describes propeller dynamicrange, detected motor currents, and motor rotational speeds, determinesthe aerodynamic power P_(a,n).
 27. A system comprising two or moremulticopters as claimed in claim 21, wherein the multicopters are eachembodied and configured to exchange data with one another in a datanetwork and the multicopters transmit respectively determined windspeed: v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B))) torespective other multicopters.
 28. The system as claimed in claim 27,wherein the multicopters are embodied as agents or softbots for wirelesscommunication in the data network.
 29. The system as claimed in claim27, wherein the system comprises a control system to control andregulate the electric motors MOT_(n) of a respective multicopter,wherein the control system is embodied and configured in such a way thatdetermined wind speeds transmitted from other multicopters:v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B))) are takeninto consideration in regulation of the electric motors MOT_(n) of therespective multicopter.
 30. The system as claimed in claim 27, whereinthe multicopters transmit positions r_(B) of the center of gravity Band/or the time derivatives: {dot over (r)}_(B) and/or {umlaut over(r)}_(B) and/or the 3D orientation o_(M) and/or the time derivative {dotover (o)}_(M) of a respective multicopter and/or the force screws τ_(e)acting externally on a respective multicopter and/or the aerodynamicpower P_(a,n) to respective other multicopters.
 31. The system asclaimed in claim 27, wherein one or more multicopters and/or a controlcenter, which is configured for data exchange with the multicopters inthe data network, is/are configured and embodied to solve anoptimization problem according to claim
 21. 32. A method of measuringwind speed v_(w) using a multicopter, wherein the multicopter has anumber N of electric motors MOT_(n) for driving N propellers PROP_(n),where n=1, 2, . . . , N and N≥2, the method comprising: providing firsttime-dependent parameters P1 comprising: a 3D position r_(B)=(x_(b),y_(b), z_(b)) of a center of gravity B of the multicopter, timederivatives {dot over (r)}_(B) and {umlaut over (r)}_(B), a 3Dorientation o_(M)=(α_(M), β_(M), γ_(M)) of the multicopter, and timederivative {dot over (o)}_(M) of the 3D orientation o_(M); providing anaerodynamic power P_(a,n) generated by the respective propellersPROP_(n); on the basis of the first parameters P1 and/or a providedmodel M1 that describes dynamics of the multicopter and/or an estimationdetermined on the basis of the model M1 of a force screw τ_(e) actingexternally on the multicopter, determining horizontal components(v_(r,x), v_(r,y)) of a relative speed v_(r) of the multicopter inrelation to air; on the basis of the determined horizontal components(v_(r,x), v_(r,y)) and the aerodynamic power P_(a,n), determining avertical component (v_(r,z)) of the relative speed v_(r), and on thebasis of the determined relative speed v_(r)=(v_(r,x), v_(r,y), v_(r,z))and on the basis of the parameters P1, determining wind speed v_(w) inan inertial system; and storing wind speed v_(w)(r_(B))=(v_(w,x)(r_(B)),v_(w,y)(r_(B)), v_(w,z)(r_(B))) determined for position r_(B) and/ortransmitting the wind speed v_(w)(r_(B)) to a receiver.
 33. The methodas claimed in claim 32, wherein the method further comprises: providinga control system to control and regulate the electric motors MOT_(n);and regulating the electric motors MOT_(n) in such a way that projectionof the wind speed v_(w) on direction of an axis of rotation of thepropellers is maximized.
 34. The method as claimed in claim 32, in whichto determine the aerodynamic power P_(a,n) per electric motor MOT_(n),the method further comprises: determining a motor current and a motorrotational speed; and on the basis of a predetermined model M2 thatdescribes the propeller dynamic range, detected motor currents, andmotor rotational speeds, determining the aerodynamic power P_(a,n). 35.A non-transitory computer-readable storage medium comprisinginstructions for measuring wind speed v_(w) using a multicopter, whereinthe multicopter has a number N of electric motors MOT_(n) for driving Npropellers PROP_(n), where n=1, 2, . . . , N and N≥2, wherein theinstructions, when executed by a computing device, cause the computingdevice to perform operations comprising: providing first parameters P1comprising: a 3D position r_(B)=(x_(b), y_(b), z_(b)) of a center ofgravity B of the multicopter, time derivatives {dot over (r)}_(B) and{umlaut over (r)}_(B), a 3D orientation o_(M)=(α_(M), β_(M), γ_(M)) ofthe multicopter, and a time derivative {dot over (o)}_(M) of the 3Dorientation o_(M); providing an aerodynamic power P_(a,n) presentlygenerated by the respective propellers PROP_(n); on the basis of thefirst parameters P1 and/or the aerodynamic power P_(a,n) and/or anestimation of one or more force screws τ_(e) acting externally on themulticopter, determining a relative speed v_(r):=(v_(r,x), v_(r,y),v_(r,z)) of the multicopter in relation to air; on the basis of thedetermined relative speed v_(r):=(v_(r,x), v_(r,y), v_(r,z))^(T) and onthe basis of the parameters P1, determining wind speed v_(w) in aninertial system; and storing wind speeds v_(w)(r_(B))=(v_(w,x)(r_(B)) ,v_(w,y)(r_(B)), v_(w,z)(r_(B))) determined for positions r_(B) and/orwirelessly transmitting the wind speeds v_(w)(r_(B)) to a receiver. 36.A non-transitory computer-readable storage medium comprisinginstructions for measuring wind speed v_(w) using a multicopter, whereinthe multicopter has a number N of electric motors MOT_(n) for driving Npropellers PROP_(n), where n=1, 2, . . . , N and N≥2, wherein theinstructions, when executed by a computing device, cause the computingdevice to perform operations comprising: providing first time-dependentparameters P1 comprising: a 3D position r_(B)=(x_(b), y_(b), z_(b)) of acenter of gravity B of the multicopter, time derivatives {dot over(r)}_(B) and {umlaut over (r)}_(B), a 3D orientation o_(M)=(α_(M),β_(M), γ_(M)) of the multicopter, and time derivative {dot over (o)}_(M)of the 3D orientation o_(M); providing an aerodynamic power P_(a,n)generated by the respective propellers PROP_(n); on the basis of thefirst parameters P1 and/or a provided model M1 that describes dynamicsof the multicopter and/or an estimation determined on the basis of themodel M1 of a force screw τ_(e) acting externally on the multicopter,determining horizontal components (v_(r,x), v_(r,y)) of a relative speedv_(r) of the multicopter in relation to air; on the basis of thedetermined horizontal components (v_(r,x), v_(r,y)) and the aerodynamicpower P_(a,n), determining a vertical component (v_(r,z)) of therelative speed v_(r), and on the basis of the determined relative speedv_(r)=(v_(r,x), v_(r,y), v_(r,z)) and on the basis of the parameters P1,determining wind speed v_(w) in an inertial system; and storing windspeed v_(w)(r_(B))=(v_(w,x)(r_(B)), v_(w,y)(r_(B)), v_(w,z)(r_(B)))determined for position r_(B) and/or transmitting the wind speedv_(w)(r_(B)) to a receiver.